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作者：Castillo, Ismael
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when strong measures of distances, such as the sup-norm, are considered. In particular, we show that likelihood methods can achieve optimal minimax sup-norm rates in density estimation on the unit interval. The introduced methodology is used to prove that commonly used families of prior distributions on densities, namely log-density pri...
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作者：Groeneboom, Piet
作者单位：Delft University of Technology
摘要：We study the maximum smoothed likelihood estimator (MSLE) for interval censoring, case 2, in the so-called separated case. Characterizations in terms of convex duality conditions are given and strong consistency is proved. Moreover, we show that, under smoothness conditions on the underlying distributions and using the usual bandwidth choice in density estimation, the local convergence rate is n(-2/5) and the limit distribution is normal, in contrast with the rate n(-1/3) of the ordinary maxim...
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作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility, obtaining convergence rates as goo...
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作者：Jirak, Moritz; Meister, Alexander; Reiss, Markus
作者单位：Humboldt University of Berlin; University of Rostock
摘要：We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function f and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of this paper is to construct an adaptive estimator for the regression function f. In contrast to the standard model where local averaging is fruitful, the nonregular conditions require a substantial different treatment based on local extreme values. We study this m...
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作者：Celisse, Alain
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille
摘要：We analyze the performance of cross-validation (CV) in the density estimation framework with two purposes: (i) risk estimation and (ii) model selection. The main focus is given to the so-called leave-p-out CV procedure (Lpo), where p denotes the cardinality of the test set. Closed-form expressions are settled for the Lpo estimator of the risk of projection estimators. These expressions provide a great improvement upon V-fold cross-validation in terms of variability and computational complexity...
